A special irreducible matrix representation of the real Clifford algebra C(3,1)

4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4x4 Dirac matrices (Majorana representation) which may prove useful in the future. As a byproduct, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras.Comment: 23 pages LaTeX, to appear in the J. Math. Phys. (v2: appendix B on Pauli matrices and references are added, minor other changes

Surprises in the doping dependence of the Fermi surface in Bi(Pb)-2212

A detailed and systematic ARPES investigation of the doping-dependence of the normal state Fermi surface (FS) of modulation-free (Pb,Bi)-2212 is presented. The FS does not change in topology away from hole-like at any stage. The data reveal, in addition, a number of surprises. Firstly the FS area does not follow the usual curve describing Tc vs x for the hole doped cuprates, but is down-shifted in doping by ca. 0.05 holes per Cu site, indicating either the break-down of Luttinger's theorem or the consequences of a significant bi-layer splitting of the FS. Secondly, the strong k-dependence of the FS width is shown to be doping independent. Finally, the relative strength of the shadow FS has a doping dependence mirroring that of Tc.Comment: 5 pages, 4 figures (revtex

Engineering Silicon Nanocrystals: Theoretical study of the effect of Codoping with Boron and Phosphorus

We show that the optical and electronic properties of nanocrystalline silicon can be efficiently tuned using impurity doping. In particular, we give evidence, by means of ab-initio calculations, that by properly controlling the doping with either one or two atomic species, a significant modification of both the absorption and the emission of light can be achieved. We have considered impurities, either boron or phosphorous (doping) or both (codoping), located at different substitutional sites of silicon nanocrystals with size ranging from 1.1 nm to 1.8 nm in diameter. We have found that the codoped nanocrystals have the lowest impurity formation energies when the two impurities occupy nearest neighbor sites near the surface. In addition, such systems present band-edge states localized on the impurities giving rise to a red-shift of the absorption thresholds with respect to that of undoped nanocrystals. Our detailed theoretical analysis shows that the creation of an electron-hole pair due to light absorption determines a geometry distortion that in turn results in a Stokes shift between adsorption and emission spectra. In order to give a deeper insight in this effect, in one case we have calculated the absorption and emission spectra going beyond the single-particle approach showing the important role played by many-body effects. The entire set of results we have collected in this work give a strong indication that with the doping it is possible to tune the optical properties of silicon nanocrystals.Comment: 14 pages 19 figure

An ARPES view on the high-Tc problem: phonons vs spin-fluctuations

We review the search for a mediator of high-Tc superconductivity focusing on ARPES experiment. In case of HTSC cuprates, we summarize and discuss a consistent view of electronic interactions that provides natural explanation of both the origin of the pseudogap state and the mechanism for high temperature superconductivity. Within this scenario, the spin-fluctuations play a decisive role in formation of the fermionic excitation spectrum in the normal state and are sufficient to explain the high transition temperatures to the superconducting state while the pseudogap phenomenon is a consequence of a Peierls-type intrinsic instability of electronic system to formation of an incommensurate density wave. On the other hand, a similar analysis being applied to the iron pnictides reveals especially strong electron-phonon coupling that suggests important role of phonons for high-Tc superconductivity in pnictides.Comment: A summary of the ARPES part of the Research Unit FOR538, http://for538.wmi.badw.d